Identifiability of an X-Rank Decomposition of Polynomial Maps

Pierre Comon 1 Yang Qi 2 Konstantin Usevich 1
1 GIPSA-CICS - CICS
GIPSA-DIS - Département Images et Signal
Abstract : In this paper, we study a polynomial decomposition model that arises in problems of system identification, signal processing and machine learning. We show that this decomposition is a special case of the X-rank decomposition --- a powerful novel concept in algebraic geometry that generalizes the tensor CP decomposition. We prove new results on generic/maximal rank and on identifiability of a particular polynomial decomposition model. In the paper, we try to make results and basic tools accessible for general audience (assuming no knowledge of algebraic geometry or its prerequisites).
Type de document :
Article dans une revue
SIAM Journal on Applied Algebra and Geometry, SIAM, 2017, 1 (1), pp.388 - 414. 〈https://epubs.siam.org/toc/sjaabq/1/1〉. 〈10.1137/16M1108388〉
Liste complète des métadonnées

https://hal.archives-ouvertes.fr/hal-01763858
Contributeur : Pierre Comon <>
Soumis le : mercredi 11 avril 2018 - 14:48:00
Dernière modification le : mardi 10 juillet 2018 - 01:18:12

Lien texte intégral

Identifiants

Collections

Citation

Pierre Comon, Yang Qi, Konstantin Usevich. Identifiability of an X-Rank Decomposition of Polynomial Maps. SIAM Journal on Applied Algebra and Geometry, SIAM, 2017, 1 (1), pp.388 - 414. 〈https://epubs.siam.org/toc/sjaabq/1/1〉. 〈10.1137/16M1108388〉. 〈hal-01763858〉

Partager

Métriques

Consultations de la notice

104